pacman::p_load(sf, raster, spatstat, tmap, tidyverse, maptools)Hands-on Exercise 02B
2nd Order Spatial Point Patterns Analysis Methods
1. Overview
Spatial Point Pattern Analysis is the evaluation of the pattern or distribution, of a set of points on a surface. In this exercise, we aim to discover the spatial point processes of childcare centers in Singapore.
The specific questions we want to answer are the following: - Are childcare centers in Singapore randomly distributed throughout the country? - If the answer to above qns is No, the next logical qns is where are the locations with higher concentration of childcare centers?
2. Data
We will be using 3 data sets: - CHILDCARE, a point feature data providing both location and attribute information of childcare centres - MP14_SUBZONE_WEB_PL, a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data - CostalOutline, a polygon feature data showing the national boundary of Singapore
3. Installing & Loading R Packages
We will be using 5 R packages -> sf, spatstat, raster, maptools and tmap.
The code chunk below is used to install and launch the 5 R packages:
4. Spatial Data Wrangling
4.1 Importing Spatial Data
We will be using st_read() of sf package to import 3 geospatial data sets into R.
childcare_sf <- st_read("data/child-care-services-geojson.geojson") %>%
st_transform(crs = 3414)Reading layer `child-care-services-geojson' from data source
`C:\byebhai8\ISSS626-GeospatialAnalytics\Hands-On_Ex\Hands-on_Ex02\data\child-care-services-geojson.geojson'
using driver `GeoJSON'
Simple feature collection with 1545 features and 2 fields
Geometry type: POINT
Dimension: XYZ
Bounding box: xmin: 103.6824 ymin: 1.248403 xmax: 103.9897 ymax: 1.462134
z_range: zmin: 0 zmax: 0
Geodetic CRS: WGS 84sg_sf <- st_read(dsn = "data", layer="CostalOutline")Reading layer `CostalOutline' from data source
`C:\byebhai8\ISSS626-GeospatialAnalytics\Hands-On_Ex\Hands-on_Ex02\data'
using driver `ESRI Shapefile'
Simple feature collection with 60 features and 4 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 2663.926 ymin: 16357.98 xmax: 56047.79 ymax: 50244.03
Projected CRS: SVY21mpsz_sf <- st_read(dsn = "data",
layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`C:\byebhai8\ISSS626-GeospatialAnalytics\Hands-On_Ex\Hands-on_Ex02\data'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Before we use these data sets, we need to ensure that they are projected in the same projection system.
st_crs(childcare_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]st_crs(sg_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]st_crs(mpsz_sf)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]Notice that except childcare_sf, both mpsz_sf and sg_sf don’t have proper crs information. As such, we will be assigning the correct crs to both the mpsz_sf and sg_sf simple feature data frames.
sg_sf3414 <- st_set_crs(sg_sf, 3414)Warning: st_crs<- : replacing crs does not reproject data; use st_transform for
thatst_crs(sg_sf3414)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]mpsz_sf3414 <- st_set_crs(mpsz_sf, 3414)Warning: st_crs<- : replacing crs does not reproject data; use st_transform for
thatst_crs(mpsz_sf3414)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]4.2 Mapping Geospatial Data Sets
It is useful to plot a map to show the spatial patterns of each geospatial data frame.
plot(sg_sf3414)
plot(mpsz_sf3414)Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
tmap_mode('view')tmap mode set to interactive viewingtm_shape(childcare_sf)+
tm_sf()tmap_mode('view')tmap mode set to interactive viewingtm_shape(childcare_sf)+
tm_dots()tmap_mode('plot')tmap mode set to plotting5. Geospatial Data Wrangling
5.1 Converting from sf format into spatstat’s ppp format
The code chunk below uses as.ppp() of spatstat to convert the spatial data into spatstat’s ppp object format:
childcare_ppp <- as.ppp(childcare_sf)Warning in as.ppp.sf(childcare_sf): only first attribute column is used for
markschildcare_pppMarked planar point pattern: 1545 points
marks are of storage type 'character'
window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] unitsLet’s plot the childcare_ppp and examine the difference:
plot(childcare_ppp)Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 1545 symbols are shown in the symbol map
The code chunk below retrieves the summary statistics of the newly created ppp object:
summary(childcare_ppp)Marked planar point pattern: 1545 points
Average intensity 1.91145e-06 points per square unit
Coordinates are given to 11 decimal places
marks are of type 'character'
Summary:
Length Class Mode
1545 character character
Window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units
(34200 x 23630 units)
Window area = 808287000 square units5.2 Handling Duplicated Points
We can use the code chunk below to check for duplication in a ppp object:
any(duplicated(childcare_ppp))[1] FALSEWe can use the code chunk below to count the number of co-incidence points:
multiplicity(childcare_ppp) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1407] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1481] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1We can use the code chunk below to find out how many locations have more than one point event:
sum(multiplicity(childcare_ppp) > 1)[1] 0We can use the code chunk below to view the locations of duplicate point events:
tmap_mode('view')tmap mode set to interactive viewingtm_shape(childcare_sf) +
tm_dots(alpha=0.4,
size=0.05)tmap_mode('plot')tmap mode set to plottingJittering - this will add a small perturbation to the duplicate points so that they do not occupy the same exact space.
The code chunk below implements the jittering approach:
childcare_ppp_jit <- rjitter(childcare_ppp,
retry=TRUE,
nsim=1,
drop=TRUE)The code chunk below helps to check if there are any duplicated points in this:
any(duplicated(childcare_ppp_jit))[1] FALSE5.3 Creating owin object
The code chunk below is used to convert sg Spatial Polygon object into an owin object of spatstat:
sg_owin <- as.owin(sg_sf)The output object can be displayed using the plot() function:
plot(sg_owin)
summary(sg_owin)Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.4015.4 Combining point events object & owin object
We will extract childcare events that are located within Singapore using the code chunk below:
childcareSG_ppp = childcare_ppp[sg_owin]The output object combines both the point and polygon feature into one ppp object:
summary(childcareSG_ppp)Marked planar point pattern: 1545 points
Average intensity 2.129929e-06 points per square unit
Coordinates are given to 11 decimal places
marks are of type 'character'
Summary:
Length Class Mode
1545 character character
Window: polygonal boundary
50 separate polygons (1 hole)
vertices area relative.area
polygon 1 (hole) 30 -7081.18 -9.76e-06
polygon 2 55 82537.90 1.14e-04
polygon 3 90 415092.00 5.72e-04
polygon 4 49 16698.60 2.30e-05
polygon 5 38 24249.20 3.34e-05
polygon 6 976 23344700.00 3.22e-02
polygon 7 721 1927950.00 2.66e-03
polygon 8 1992 9992170.00 1.38e-02
polygon 9 330 1118960.00 1.54e-03
polygon 10 175 925904.00 1.28e-03
polygon 11 115 928394.00 1.28e-03
polygon 12 24 6352.39 8.76e-06
polygon 13 190 202489.00 2.79e-04
polygon 14 37 10170.50 1.40e-05
polygon 15 25 16622.70 2.29e-05
polygon 16 10 2145.07 2.96e-06
polygon 17 66 16184.10 2.23e-05
polygon 18 5195 636837000.00 8.78e-01
polygon 19 76 312332.00 4.31e-04
polygon 20 627 31891300.00 4.40e-02
polygon 21 20 32842.00 4.53e-05
polygon 22 42 55831.70 7.70e-05
polygon 23 67 1313540.00 1.81e-03
polygon 24 734 4690930.00 6.47e-03
polygon 25 16 3194.60 4.40e-06
polygon 26 15 4872.96 6.72e-06
polygon 27 15 4464.20 6.15e-06
polygon 28 14 5466.74 7.54e-06
polygon 29 37 5261.94 7.25e-06
polygon 30 111 662927.00 9.14e-04
polygon 31 69 56313.40 7.76e-05
polygon 32 143 145139.00 2.00e-04
polygon 33 397 2488210.00 3.43e-03
polygon 34 90 115991.00 1.60e-04
polygon 35 98 62682.90 8.64e-05
polygon 36 165 338736.00 4.67e-04
polygon 37 130 94046.50 1.30e-04
polygon 38 93 430642.00 5.94e-04
polygon 39 16 2010.46 2.77e-06
polygon 40 415 3253840.00 4.49e-03
polygon 41 30 10838.20 1.49e-05
polygon 42 53 34400.30 4.74e-05
polygon 43 26 8347.58 1.15e-05
polygon 44 74 58223.40 8.03e-05
polygon 45 327 2169210.00 2.99e-03
polygon 46 177 467446.00 6.44e-04
polygon 47 46 699702.00 9.65e-04
polygon 48 6 16841.00 2.32e-05
polygon 49 13 70087.30 9.66e-05
polygon 50 4 9459.63 1.30e-05
enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
(53380 x 33890 units)
Window area = 725376000 square units
Fraction of frame area: 0.401plot(childcareSG_ppp)Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 1545 symbols are shown in the symbol map
The code chunk below will be used to extract the target planning areas:
pg <- mpsz_sf %>%
filter(PLN_AREA_N == "PUNGGOL")
tm <- mpsz_sf %>%
filter(PLN_AREA_N == "TAMPINES")
ck <- mpsz_sf %>%
filter(PLN_AREA_N == "CHOA CHU KANG")
jw <- mpsz_sf %>%
filter(PLN_AREA_N == "JURONG WEST")Plotting the target planning areas:
par(mfrow=c(2,2))
plot(pg, main = "Ponggol")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
plot(tm, main = "Tampines")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
plot(ck, main = "Choa Chu Kang")Warning: plotting the first 10 out of 15 attributes; use max.plot = 15 to plot
all
plot(jw, main = "Jurong West")Warning: plotting the first 9 out of 15 attributes; use max.plot = 15 to plot
all
Now we will convert these sf objects into owin objects:
pg_owin = as.owin(pg)
tm_owin = as.owin(tm)
ck_owin = as.owin(ck)
jw_owin = as.owin(jw)The code chunk below will help extract childcare that is within the specific region:
childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]Next, rescale() function will be used to transform the unit of measurement from metre to kilometre:
childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")The code chunk below is used to plot these 4 study areas and the locations of the childcare centers:
par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 60 symbols are shown in the symbol mapplot(childcare_tm_ppp.km, main="Tampines")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 89 symbols are shown in the symbol mapplot(childcare_ck_ppp.km, main="Choa Chu Kang")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 61 symbols are shown in the symbol mapplot(childcare_jw_ppp.km, main="Jurong West")Warning in default.charmap(ntypes, chars): Too many types to display every type
as a different characterWarning: Only 10 out of 88 symbols are shown in the symbol map
6. 2nd Order Spatial Point Patterns Analysis
6.1 Analysing using G-Function
The G function measures the distribution of the distances from an arbitrary event to its nearest event.
The code chunk below is used to compute G-function using Gest() of spatstat package:
G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Choa Chu Kang are randomly distributed
H1 = The distribution of childcare services at Choa Chu Kang are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
We will perform the Monte Carlo test with G-function:
G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.plot(G_CK.csr)
Computing G-function estimation:
G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Tampines are randomly distributed
H1 = The distribution of childcare services at Tampines are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.plot(G_tm.csr)
6.2 Analysing using F-Function
The F-function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape.
The code chunk below is used to compute F-function using Fest() of spatstat package:
F_CK = Fest(childcare_ck_ppp)
plot(F_CK)
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Choa Chu Kang are randomly distributed
H1 = The distribution of childcare services at Choa Chu Kang are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
We will perform the Monte Carlo test with F-function:
F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.plot(F_CK.csr)
Computing F-function estimation:
F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Tampines are randomly distributed
H1 = The distribution of childcare services at Tampines are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)Generating 999 simulations of CSR ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.
Done.plot(F_tm.csr)
6.3 Analysing using K-Function
K-function measures the number of events found up to a given distance of any particular event.
Computing K-function estimate:
K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Choa Chu Kang are randomly distributed
H1 = The distribution of childcare services at Choa Chu Kang are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")
Computing K-function estimate:
K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r,
ylab= "K(d)-r", xlab = "d(m)",
xlim=c(0,1000))
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Tampines are randomly distributed
H1 = The distribution of childcare services at Tampines are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.plot(K_tm.csr, . - r ~ r,
xlab="d", ylab="K(d)-r", xlim=c(0,500))
6.4 Analysing using L-Function
Computing L-function estimation:
L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)")
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Choa Chu Kang are randomly distributed
H1 = The distribution of childcare services at Choa Chu Kang are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")
Computing L-function estimate:
L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r,
ylab= "L(d)-r", xlab = "d(m)",
xlim=c(0,1000))
To confirm the observed spatial patterns above, a hypothesis test will be conducted.
The test hypotheses are:
H0 = The distribution of childcare services at Tampines are randomly distributed
H1 = The distribution of childcare services at Tampines are not randomly distributed
The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.
The code chunk below is used to perform the hypothesis testing:
L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)Generating 99 simulations of CSR ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99.
Done.The code chunk below is used to plot the model output:
plot(L_tm.csr, . - r ~ r,
xlab="d", ylab="L(d)-r", xlim=c(0,500))